if a square has length of its side is 8cm then find length of its diagonal​

Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').

Answer:

Substitute 0 for the value of x and y.

5x - 6y = 30

5x - 6(0) = 30

5x = 30

The x-intercept is 6.

x = 6

(6, 0)

5x - 6y = 30

5(0) - 6y = 30

-6y = 30

y = -5

The y-intercept is -5.

(0, -5)

(The graph is in the picture)

Nick's monthly mortgage payment is $482.16.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

To calculate Nick's monthly mortgage payment, we first need to find out the amount he borrowed from the bank, which is 75% of the purchase price:

$145,500 x 0.75 = $109,125

Next, we need to calculate the monthly interest rate. We can do this by dividing the annual interest rate (3.15%) by 12:

3.15% / 12 = 0.002625

Now we can use the following formula to calculate Nick's monthly payment:

M = P [ [tex]i(1 + i)^{n}[/tex] ] / [ [tex](1 + i)^{n}[/tex] – 1]

Where:

M = Monthly payment

P = Loan amount (principal)

i = Monthly interest rate

n = Number of payments (in months)

Plugging in the values we have:

M = $109,125 [ 0.002625 [tex](1 + 0.002625)^{360}[/tex] ] / [ [tex](1 + 0.002625)^{360}[/tex] – 1]

M = $482.16

Therefore, Nick's monthly mortgage payment is $482.16.

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Answer:

To differentiate the given expression, we will need to use both the product rule and the quotient rule.

Let's first rewrite the expression using the reciprocal identity for x:

2y/5x = 2y * (5x)^(-1)

Now we can use the product rule and the quotient rule to find the derivative with respect to x:

d/dx [2y * (5x)^(-1)] = 2y * d/dx[(5x)^(-1)] + (5x)^(-1) * d/dx[2y]

Using the chain rule, we can find the derivative of (5x)^(-1) with respect to x:

d/dx[(5x)^(-1)] = -1/(5x)^2 * 5 * (dx/dx)

d/dx[(5x)^(-1)] = -1/(5x)^2

Using the chain rule again, we can find the derivative of 2y with respect to x:

d/dx[2y] = 2 * (dy/dx)

Substituting these expressions back into the original equation, we get:

d/dx [2y/5x] = 2y * (-1/(5x)^2) + (5x)^(-1) * 2 * (dy/dx)

Simplifying this expression, we get:

d/dx [2y/5x] = -2y/(5x)^2 + 2/(5x) * (dy/dx)

Therefore, the derivative of 2y/5x with respect to x is -2y/(5x)^2 + 2/(5x) * (dy/dx).

The correct option - A) conflict of interest is caused due to ABC Ad Agency has two automotive tire chains as clients.

A conflict of interest arises when a person's personal interests, such as those related to their family, friends, finances, or social standing, potentially impair their judgement, choices, or actions at work. Conflicts of interest are taken seriously enough by government organisations that they are governed.

For the given data- The ABC Ad Agency has two automotive tire chains as clients.

This, could  lead to a(n) conflict of interest.

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Let's assume that the elevator has a weight capacity of W pounds.

We can set up two equations to represent the number of adults (A) and the number of children (C) the elevator can hold:

Averaged weight per adult * Number of adults + Averaged weight per child * Number of children ≤ Weight capacity of the elevator

Using the given values, we can substitute:

150A + 40C ≤ W

This equation represents the weight limit of the elevator, where the sum of the weight of all adults and children inside the elevator cannot exceed W.

All the intersection points are determined as (-65, 0, 3.48).

To find the intersection points of the two given functions, we can set them equal to each other and solve for the values of x and y that satisfy the equation.

Setting y = 3x² + x - 10 equal to y = x³ + 6x² + d, we get:

3x² + x - 10 = x³ + 6x² + d

Rearranging this equation, we get:

x³ + 3x² - x + d - 10 = 0 ...........(1)

Now, since we are given that the two graphs intersect at x = -5, we can substitute x = -5 into equation (1) to find the value of d.

Substituting x = -5 into equation (1), we get:

(-5)³ + 3(-5)² - (-5) + d - 10 = 0

-125 + 3(25) + 5 + d - 10 = 0

75 + d - 10 = 0

65 + d = 0

d = -65

So the value of d is -65.

Now that we have the value of d, we can substitute it back into equation (1) to find the other intersection points.

Substituting d = -65 into equation (1), we get:

x³ + 3x² - x - 75 = 0 ...........(2)

Solve equation (2), using graphing system.

roots = (3.48, 0)

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A41 represents the element at the line 4 and column 1, which is the same for B41.

When two matrices are added or subtract, we add or subtract the elements at the same position.

The elements are:

Hence:

When a matrix is multiplied by a constant, each element is multiplied by a constant, hence:

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Therefore, Fatima's monthly payment would be $460.23.

Interest is the amount of money that is charged by a lender to a borrower for the use of money or a loan. It is usually calculated as a percentage of the principal amount (the amount of money borrowed) and can be either simple or compound, depending on the type of loan. Interest is typically paid by the borrower to the lender over a set period of time, such as monthly, quarterly, or annually. The interest rate can be fixed or variable, and is determined by a variety of factors including the borrower's creditworthiness, the amount of the loan, and the length of the repayment period.

Here,

To calculate the monthly payment for a car loan, we need to use the formula:

M = P [ i(1 + i)ⁿ] / [ (1 + i)ⁿ – 1]

Where:

M = monthly payment

P = principal (the amount of the loan)

i = monthly interest rate (annual interest rate divided by 12)

n = number of months

First, we need to calculate the monthly interest rate:

i = 4.7% / 12

= 0.003917

Next, we need to calculate the number of months:

n = 5 years x 12 months/year

= 60 months

Now, we can plug in the values and solve for M:

M = 25,000 [ 0.003917(1 + 0.003917)⁶⁰ ] / [ (1 + 0.003917)⁶⁰ – 1]

M = $460.23 (rounded to the nearest cent)

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The inverse function of f(x) = 3x + 5 is given as follows:

C. p(x) = 1/3x - 5/3.

The function in the context of this problem is defined as follows:

f(x) = 3x + 5.

To obtain the inverse function, first we must exchange the variables x and y, hence:

y = 3x + 5

x = 3y + 5.

Now we must isolate the variable y, hence:

3y = x - 5

y = (x - 5)/3.

p(x) = 1/3x - 5/3.

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The investment will be worth approximately $4468 after 14 years.

Annual interest rate is the rate at which an investment or loan grows in value over the course of a year, expressed as a percentage. It represents the cost of borrowing or the return on investment over one year.

The following equation can be used to determine the future value of an investment using compound interest:

FV = P * (r/n + 1)(n*t)

Where:

FV is the investment's future value.

The principal is P. (initial investment)

The annual interest rate is represented by r,

The number of times the interest is compounded annually by n (expressed as a decimal).

t is the time (in years)

In this case:

P = $1500

r = 8.5% = 0.085

n = 1 (compounded annually)

t = 14

With these values entered into the formula, we obtain:

FV = 1500 * [tex](1 + 0.085/1)^(1*14)[/tex]

     = $4467.56

Therefore, the investment will be worth approximately $4468 after 14 years.

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As a statistical question is one that can be addressed using statistical methods or analysis, looking at the responses to a question can help identify whether it is a statistical question.

In order to provide a response to a question regarding a population or sample, statistical inquiries typically entail gathering and evaluating data. Consequently, a statistical question's responses would require some sort of data analysis or interpretation.

As a result, we can tell if a question is statistical by looking at the replies and seeing if it requires the use of statistical techniques and data analysis to answer.

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When two sample means are significantly different, "the difference is too great to attribute to chance".

The likelihood of finding a difference between two samples (such means or proportions) through pure chance is known as statistical significance. The likelihood of obtaining the observed difference if there were no actual difference between the associated population parameters is calculated to ascertain this. The difference is deemed statistically significant if the p-value is below a predetermined cutoff (often 0.05).

Significant difference between two sample means indicates that the likelihood of such a difference occurring by chance alone is low. If there is a true difference between the matching population means from which the samples were selected, it shows that the difference between the sample means is too large to be explained by chance.

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Okay, here are the steps to find the probability the randomly selected pitcher is left-handed:

1) There are 1 left-handed starter, 4 right-handed starters, 2 left-handed relievers and 1 right-handed reliever.

2) In total, there are 1 + 4 + 2 + 1 = 8 pitchers.

3) Of the 8 pitchers, 1 + 2 = 3 are left-handed.

4) So the probability the randomly selected pitcher is left-handed = (3/8) = 3/8 = 0.375

Therefore, the probability that the randomly selected pitcher from the team is left-handed is 0.375.

Let me know if you have any other questions!

a. There are twelve unique pentominos possible in all.

b. In total, only 6 pentominos have the refection symmetry.

What is a pentomino?

A pentomino is an order 5 polyomino, or a plane polygon formed of 5 identical squares joined edge to edge. This is just linked with a certain arrangement of squares.

a. There are twelve unique pentominos possible in all which on reflection and rotation can create multiple more pentominos.

b. In total, 6 pentominos have refection symmetry which means that now the total pentominos are 18 of which 6 have reflection symmetry.

Hence, the required solution has been obtained.

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The correct answer is (1,1) because both of the lines meet together at these numbers